Presentation of the CADP toolbox
CADP toolbox
What is CADP ?
LOTOS language
Tools for functional verification
CADP extended for performance evaluation
IMC formalism
From LOTOS to Markov chain
From LOTOS to Markov chain – example Tools for performance evaluation
Leiden Workshop
20/06/2007
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What is CADP?
CADP:
« Construction and Analysis of Distributed Processes »
Developped at INRIA Rhônes-Alpes (France) by the VASY
team
Toolbox for the design of communication protocols and
distributed systems.
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LOTOS language
LOTOS =
Process Algebra (CCS & CSP)
caesar compiler
+
Abstract Data Type Algebra (ACT-ONE)
caesar.adt compiler
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LOTOS language
process queue_behavior [PUSH , POP]
(SMax:Nat, Q: Queue) : noexit :=
PUSH
[getCurrentSize(Q)<SMax] ->
PUSH
PUSH;
POP
queue_behavior[PUSH , POP] (SMax,Push(Q))
[]
POP
PUSH
[getCurrentSize(Q)>0] ->
POP;
POP
queue_behavior[PUSH
, POP] (SMax,Pop(Q))
endproc
bcg format
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LOTOS language
memory
memory.bcg = generation of memory.lotos;
phys_queue.bcg = generation of phys_queue.lotos;
PUSH
TO_MEM
system.bcg =
memory.bcg
|[TO_MEM, FROM_MEM]|
phys_queue.bcg;
FROM_MEM
POP
Physical
queue.bcg = hide TO_MEM, FROM_MEM in system.bcg
queue
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Tools for functional verification
Model checking on the LTS
Various temporal logics and mu-calculus (evaluator, XTL)
Equivalence checking
Minimization and comparisons modulo bisimulations
relations
(bcg_min, bisimulator)
Simulation & co-simulation
Visual checking (bcg_edit)
Step-by-step simulation (ocis)
C simulator (caesar –simulator)
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IMC formalism
The behavior of a physical system can often be represented by :
All the states the system may occupy
How the system move from one state to another
Functional behavior: (LTS)
Composition
Concurrency
Synchronization
PUSH
↓↓↓
POP
PUSH
Description
of large
systems
&& Formal
POP verification
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action based
time based
Timed behaviour: (CTMC)
IMC
Performance
measures
No composition,
synchronization…
rate λ
rate λ
rate μ
↓↓↓
Performance evaluation
of complex systems
reserved to
rate μ
specialists
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IMC formalism
1 model
Interactive transitions
Markovian transitions
Synchronization
Composition
Functional
verification
Hiding of Markovian transitions
and minimization
LTS
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Represent delays
IMC
Performance
evaluation
Hiding of Interactive transitions
and stochastic minimization
CTMC
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From LOTOS to Markov chains
Performance evaluation with LOTOS/CADP :
Introduction of Markov transitions in LOTOS models.
≈ Introduction of delays in LOTOS models.
Identifying the start
and end of relevant
timing delays in the
model
Exposing each start
and end as LOTOS
gates
1
2
Identifying the
distribution of the
delay
Approximating the
delays as CTMC
3
Embedding each
delay into start/end
gates
4
5
=> Generation of an Interactive Markov Chain (IMC)
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From LOTOS to Markov chains
- example Time needed to process a PUSH
Time needed to process a POP
Identifying the start and
end of relevant timing
delays in the model
(λ)
(μ)
Time between 2 PUSH
Time between 2 POP
Proba
1
RQ
1
RSP
RQ
(δ1)
(δ2)
RSP
PUSH
time
Exposing each start and
end as LOTOS gates
POP
2
RQ RSP
time
RQ RSP
RQ RSP
0
GENERATOR
PUSH_RSP
δ1_START
GEN_DELAY […] :
δ1_START;
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PUSH_DELAY […] :
λ_START;
λ_DELAY;
δ1_DELAY;
δ1_STOP;
GEN_DELAY […]
PUSH_DELAY
GEN_DELAY
λ_DELAY;
λ_STOP;
PUSH_DELAY […]
CONSUMER
POP_RSP
POP_DELAY
POP_DELAY […] :
μ_START;
μ_DELAY;
μ_DELAY;
δ2_STOP
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δ1_STOP
Embedding each delay
into start/end gates
CONSUMER […] :
δ2_START;
δ2_STOP;
POP_RQ;
POP_RSP ?Elmt;
CONSUMER […]
POP_RQ
μ_START
4
QUEUE
[ PUSH_RQ, PUSH_RSP,
POP_RQ,
POP_RQ, POP_RSP,]
POP_RSP,
λ_START, λ_STOP,
μ_START, μ_STOP ]
δ2_START
PUSH_RQ
λ_START
Approximating the
delays as CTMC
GENERATOR […] :
δ1_START;
δ1_STOP;
PUSH_RQ !DATA;
PUSH_RSP;
GENERATOR […]
ENVIRONMENT
SYSTEM
μ_STOP
3
ENVIRONMENT
λ_STOP
Identifying the
distribution of the delays
CONS_DELAY […] :
δ2_START;
δ2_DELAY;
μ_STOP;
POP_DELAY […]
δ2_STOP;
CONS_DELAY […]
CONS_DELAY
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From LOTOS to Markov chains
Performance evaluation with LOTOS/CADP :
Introduction of Markov transitions in LOTOS models.
≈ Introduction of delays in LOTOS models.
Identifying the start
and end of relevant
timing delays in the
model
Exposing each start
and end as LOTOS
gates
1
2
Identifying the
distribution of the
delay
Approximating the
delays as CTMC
3
Embedding each
delay into start/end
gates
4
5
=> Generation of an Interactive Markov Chain (IMC)
Hiding of the non-Markovian transition and minimisation
=> generation of a Markov Chain (CTMC)
Performance evaluation based on the analysis of these CTMC.
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Tools for performance evaluation
Stochastic minimization (bcg_min)
Based on the maximum progress rule
=> generation of a Markov Chain (CTMC)
Performance evaluation based on the analysis of a CTMC.
Transient state probabilities (bcg_transient)
Steady state probabilities (bcg_steady)
Throughput results (-thr option)
Use of the state probabilities for more complex measures
Weighted sum of the state probabilities
Mean queue length
Mean time before failure
…
API in CADP for graph exploration for this kind of computation
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Summary : performance evaluation
my_model_with_start_and_stop_delay_gates.bcg =
generation of my_model_with_start_and_stop_delay_gates.lotos;
my_delay1.bcg = generation of my_delay1.lotos;
…
my_delayN.bcg = generation of my_delayN.lotos;
my_imc.bcg =
( ( ( my_model_with_start_and_stop_delay_gates.bcg
|[DL1_START, DL1_STOP]|
my_delay1.bcg
)
|[...]|
…
)
|[DLN_START, DLN_STOP]|
my_delayN.bcg
);
my_mc.bcg = stochastic reduction of hide …. in my_imc.bcg
%bcg_steady –sol my_mc.sol my_mc.bcg
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Conclusion
More information at :
http://www.inrialpes.fr/vasy/cadp/
free of charge for universities and public research centers
Toolbox written in C and available for:
Solaris
Linux
Windows
MacOS
Questions ?
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